We present an efficient algorithm for the problem of online multiclass prediction with bandit feedback in the fully adversarial setting. We measure its regret with respect to the log-loss defined in (Abernethy and Rakhlin, 2009), which is parameterized by a scalar $$\alpha$$. We prove that the regret of Newtron is $$O(\log T)$$ when $$\alpha$$ is a constant that does not vary with horizon $$T$$, and at most $$O(T^{2/3})$$ if $$\alpha$$ is allowed to increase to infinity with $$T$$. For $$\alpha = O(\log T)$$, the regret is bounded by $$O(\sqrt{T})$$, thus solving the open problem of Kakade et al (2008) and Abernethy and Rakhlin (2009). Our algorithm is based on a novel application of the online Newton method (Hazan et al, 2007). We test our algorithm and show it to perform well in experiments, even when $$\alpha$$  is a small constant.